Answer:
[tex]\huge\boxed{b.\ x=6;\ y=3}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x=2y&(1)\\2x+3y=21&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\2(2y)+3y=21\\4y+3y=21\qquad\text{combine like terms}\\7y=21\qquad\text{divide both sides by 7}\\\dfrac{7y}{7}=\dfrac{21}{7}\\\boxed{y=3}\\\\\text{Substitute it to (1):}\\x=2(3)\\\boxed{x=6}[/tex]
Answer: (6, 3)
Explanation: Our first equation tells us that x means the same thing as 2y so we can replace the x in the second equation with a 2y.
Our second equation then becomes 2(2y) + 3y = 21.
If we simplify on the left side we get
4y + 3y = 21 which simplifies to 7y = 21.
Solving from here, we find that y = 3.
To find x, plug 3 back in for y in the first equation
to get x = 2(3) which simplifies to x = 6.
So our answer is (6, 3).
Which is a correct step to solve the equation 1=−4+3/8x
A.4(1)=4(−4+3/8x)
B.1=8(−4+3/8x)
C.8(1)=8(−4+3/8x)
D.3(1)=3(−4+3/8x
Can someone please help me
Answer:
C. 8(1)=8(−4+3/8x)
Step-by-step explanation:
Given equation
1=−4+3/8x
in this equation in denominator we have 8x,
since we are solving for x we cannot eliminate it, but we have to eliminate 8 in denominator, so that there only numerator in equation and solving process becomes easier.
To eliminate 8,we need to multiply both side by 8, so as to balance the equation and also 8 from denominator gets cancelled in RHS.
1=−4+3/8x
multiply both side by 8
8(1)=8(−4+3/8x)
Thus, option c is correct one
8(1)=8(−4+3/8x)
solving it
8 = -32 + 3/x
adding both side 32
8+32 = -32 + 3/x -32
=> 40 = 3/x
=> x = 3/40
Please help and explain!! I really don't get this
In circle Y, what is m∠1? 6° 25° 31° 37°
Answer:
option c (31)
Step-by-step explanation:
Given: f(x) = x2, g(x) = x + 6, h(x) = 7
Find g{fſh(x)}}.
20
169
55
Answer:
20 or 55
Step-by-step explanation:
It depends because i am not sure what f(x) is.
Case 1: f(x)=x^2
We know h(x)=7 hence f(h(x))=7^2=49 hence g(f(h(x)))=49+6=55
Case 2: f(x)=x*2
We know h(x)=7 hence f(h(x))=2*7=14 hence g(f(h(x)))=14+6=20
Note: x^2 is x to the power of 2 while x*2 is x times 2.
Please answer both questions
Answer:
which question......
In the school election, votes were cast for Sam, Mary, and Bill in the ratio 4:3:2. If a total of 2178 votes were cast, how many votes did Mary receive?
Answer:
Step-by-step explanation:
Mary received 726 votes.
which statements are true for the function g(x)=x^2 and h(x)=-x^2? check all tht apply
Answer:
where are the statements...
mention the statements first
In a newspaper, it was reported that the number of yearly robberies in Springfield in 2013 was 100, and then went up by 25% in 2014. How many robberies were there in Springfield in 2014?
Answer:
125
Step-by-step explanation:
So saying something went up by 25% means that it is essentially
X + .25X
So in this case X = 100 and .25X = 25
So 100 + 25 = 125
oops i did something wrong last question cuz it accidentally showed my email
Answer:
A, D and E
Step-by-step explanation:
Option B is an inequality while Option C is an Equation. However, Rest of the options are expressions because they don't have any equality (=) sign or any inequality (<,>,≥,≤). So, they are expressions.
Does anyone know this need help please!!!!!!! Hurry thanks
Answer:
Add the two equations: 5y=5 so y=1, therefore x=3-2y=1.
What did you mean by Dx? If it's the determinant for x then it's:
| 3 2 |
| 2 3 | = 9-4=5
Dy is:
| 1 3 |
| -1 2 | = 2-(-3)=5
And D is:
| 1 2 |
| -1 3 | = 3-(-2)=5
x=Dx/D=5/5=1 and y=Dy/D=5/5=1
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind only 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Answer:
The speed of plane = 40 m/s
The speed of the wind = 300 m/s
Step-by-step explanation:
Let the speed of the plane = Y
And the speed of the wind = X
If the plane then travel 340 miles per hour with the wind, that means the plane and the wind are moving in the same direction. Therefore,
X + Y = 340 ..... ( 1 )
Also, 260 miles per hour against the wind. That is, the plane is moving opposite to the direction of the wind. Therefore,
X - Y = 260 ..... ( 2 )
Solve the two equations simultaneously by addition. That will eliminate Y
X + Y = 340
X - Y = 260
2X = 600
X = 600/2
X = 300 m/s
Substitutes X in equation (1)
300 + Y = 340
Make Y the subject of formula by collecting the like terms
Y = 340 - 300
Y = 40 m/s
Therefore, the speed of the plane is 40 m/s. While the speed of the wind is 300 m/s.
Point D is on segment BC, Segment BC measures Bx
units in length
What is the length of segment BC?
units
Answer:
144 units
Step-by-step explanation:
3x + 8 + 4x + 10 = 8x
7x + 18 = 8x
8x - 7x = 18
x = 18
8x is length of BC
8 × 18 is length of BC
144 units
Answer:
What is the length of segment BC?
144 units
explanation:
<3
(will mark brainliest if correct)
Answer:
A = 27π
P =
Step-by-step explanation:
Well if it follows the same proportions as a square then the dotted line is 6 cm.
Triangle
So the area of a triangle is b*h / 2
b = 6
h = 6
6*6 = 36
36 / 2 = 18
A = 18cm^2
So to find the missing side or c we do 6^2 + 6^2 = c^2,
36 + 36 = c^2
72 = c^2
≅8
6 + 6 + 8
= 20cm
Half circle
Now the area of a semicircle is,
pi r^2 / 2
So if the diameter is 6 then the radius is 3.
So we do 3*3 = 9
9 * pi = 9π^2
Perimeter: 6π
____________________________________________________________
Thus,
the area is 27π and the perimeter 26π.
Hope this helps :)
Solve for x in the diagram below.
Answer:
x= 20
Step-by-step explanation:
The three angles add to 90 degrees
x+2x+x+10 = 90
Combine like terms
4x+10 = 90
Subtract 10 from each side
4x +10-10 = 90-10
4x = 80
Divide by 4
4x/4 = 80/4
x = 20
Answer:
x = 20
Step-by-step explanation:
The three angles are complementary to each other.
That means they add up to 90 degrees.
x + 2x + (x + 10) = 90
Combine like terms.
4x + 10 = 90
Subtract 10 on both sides.
4x = 80
Divide both sides by 4.
x = 20
3 sides of the triangle are distinct prime numbers. What is the smallest possible perimeter of the triangle?
Answer:
the smallest possible perimeter is 6
Step-by-step explanation:
since the smallest possible prime number is 2 it would make since if each side is 2 which makes the smallest perimeter possible. i really hope this helped :)
Answer:
6
Step-by-step explanation:
the smallest possible number will be 2.
2 inches/centimeters of each 3 sides of the triangle
Debby pays rent twice a year, buys groceries once every quarter, and buys a transit pass
every month. How should her yearly expenses be represented?
1. O2 + 4y + 122
2. O 2x + 4y + 12z
3. OI +y + 122
4. O 2x + 3y + 12z
Work Shown:
x = amount of rent paid per half year
2x = amount of rent paid annually
y = amount spent on groceries per quarter
4y = amount spent on groceries annually
z = amount spent on a transit pass monthly
12z = amount spent on transit pass annually
2x+4y+12z = total amount of money spent annually
Answer:
2x+4y+12z
Step-by-step explanation:
I just did the test and got it right
What is the difference between a Rate and a Ratio? Explain *
Answer:
Step-by-step explanation:
A ratio is a comparison of two numbers. A ratio can be written using a colon, 8:12 , or as a fraction 8/12 . A rate is a comparison of two quantities which can have different units. For example 8 miles per 4 hours is a rate.
Consider 8x2 - 48x = -104. Write the equation so that a = 1: x2 + __ x = __
Answer:
x² + -6x = -13
Step-by-step explanation:
8x² - 48x = -104
x² - 6x = -13
The quadratic equation can be written as x² + (- 6x) = - 13
Quadratic equations are algebraic expressions which the highest value of x in its second degree. It is usually expressed in the form: ax² + bx + c
From the given information, the objective is to simplify the quadratic equation in terms of ax² + bx + c
∴
ax² + bx = cGiven that:
8x² - 48x = -104We need to divide through by (8)
[tex]\mathbf{\dfrac{8x^2}{8} - \dfrac{48x}{8} = -\dfrac{104}{8}}[/tex]x² + (- 6x) = - 13Learn more about quadratic equations here:
https://brainly.com/question/1214333
phillp asked 100 students they favourite crisps out of ready salted, cheese and onion, and salt and vinegar. 35 students are boys 12 of these boys liked cheese and onion the best 9 girls liked ready salted the best 25 out of 41 students woh liked salt and vinger the best were girls work out the total number of students who liked ready salted the best.
Answer:16 students liked ready salted
Step-by-step explanation:
35 students = boys
65 students = girls
Boys:
12/35 like cheese and onion
16/35 like salt and vinegar
7/35 like ready salted
Girls:
9/65 like ready salted
25/65 like salt and vinegar
31/65 like cheese and onion
Question 8 Multiple Choice Worth 1 points)
(03.08 MC)
Two different plants that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the height of the
f(x) plant exceed that of the g(x) plant?
Month (x) f(x) = 3* g(x) = 5x + 12
1
3
17
2.
9
22
O Month 3
O Month 4
O Month 5
O Month 6
Answer:
Option B.
Step-by-step explanation:
Note: The function f(x) is not in correct format it must be [tex]f(x)=3^x[/tex].
It is given that two different plants that grow each month at different rates are represented by the functions f(x) and g(x).
Let as consider the two functions,
[tex]f(x)=3^x[/tex]
[tex]g(x)=5x+12[/tex]
Now, table of values is
Month(x) [tex]f(x)=3^x[/tex] [tex]g(x)=5x+12[/tex]
1 3 17
2 9 22
3 27 27
4 81 32
From the above table it is clear that in first and second month the height of the f(x) plant is less than of g(x).
In month 3, heights are equal.
In month 4, height of the f(x) plant exceed that of the g(x) plant.
Therefore, the correct option is B.
Triangle ABC has vertex coordinates A(–5, 2), B(–1, 3), and C(–1, 1). It is rotated 90° clockwise around the origin. What are the coordinates of B'?
Answer:
(3,1)
Step-by-step explanation:
The rule for a 90 degree clockwise rotation:
[tex](x,y)\rightarrow(y,-x)[/tex]
B is (-1, 3).
Apply the rule:
[tex]\frac{(-1,3)\rightarrow\boxed{(3,1)}}{(x,y)\rightarrow(y,-x)}\\\\3 * 1 = 3\\\\-1 * -1 = 1[/tex]
Option D should be the correct answer.
A car travels at a speed of 41 meters/second using 756 joules of energy every second. Suppose we know that the car uses 52,700 joules of energy. Set up a calculation to find the number of meters the car travels with this amount of energy. Perform the calculation you set up in part A. Round your answer to the nearest whole number? What is The car will travel ??? meters using 52,700 joules of energy.
The car will travel 2858meters.
What is speed?Speed is the rate of change of distance.
Analysis:
speed of car = 41m/s
Energy consumption rate of engine = 756 joules/second
Time taken to consume 52700 joules = 52700/756.
If it travels at 41m/s for 52700/756 seconds, then the distance covered = 41 x 52700/756 = 2858 meters.
Learn more about speed: brainly.com/question/4931057
#SPJ1
Answer:
2900
Step-by-step explanation:
.
Alice is building a caterpillar habitat for some caterpillars she found in her back yard. She plans to cover all sides of the habitat with screen so the caterpillars get plenty of fresh air. What is the total amount of screen that Alice will need for her habitat? Give an exact answer (do not round).
Answer:
22ft^2
Step-by-step explanation:
I am not sure if this is the correct answer since there were no numbers to the question you wrote out.
20 points repost because no one answered. Geomertry question
Answer:
x=2.25
Step-by-step explanation:
ΔABC and ΔADE are similar.
∴ sides are proportional.
[tex]\frac{5}{1} =\frac{x+9}{x} \\5=\frac{x}{x} +\frac{9}{x} \\5=1+\frac{9}{x}\\\frac{9}{x}=5-1\\\frac{9}{x}=4\\x=\frac{9}{4}=2.25[/tex]
Answer:
x = 9/4
Step-by-step explanation:
We know that the triangles are similar
We can use ratios to solve
x x+9
----- = ----------------
1 5
Using cross products
5x = 1(x+9)
5x = x+9
Subtract x
5x-x = x+9-x
4x= 9
Divide by 4
4x/4 = 9/4
x = 9/4
The monthly salary of a salesman of a departmental store is Rs 12,500 and an additional payment of 0.5 % on the total monthly sale is provided as commission.
i) Calculate his total income in a month if he makes a total sale of Rs 7,20,000 in that month.
ii) What should be his total sale in the next month so that he can receive a total income of Rs 20,000 in the month?
Answer:
i. [tex]Total\ Income = Rs\ 16,100[/tex]
ii. [tex]Monthly\ Sales = Rs\ 1,500,000[/tex]
Step-by-step explanation:
Given
[tex]Salary = Rs\ 12,500[/tex]
Commission = 0.5% of Monthly Sales
Calculating his total income is total sales is Rs 720,000
[tex]Total\ Income = Salary + Commission[/tex]
Substitute (0.5% of Monthly Sales) for Commission
[tex]Total\ Income = Salary + (0.5\%\ of\ Monthly\ Sales)[/tex]
Substitute Rs 720,000 for Monthly Sales and Rs 12,500 for Salary
[tex]Total\ Income = Rs\ 12,500 + 0.5\%\ of\ Rs\ 720,000[/tex]
[tex]Total\ Income = Rs\ 12,500 + 0.5\%\ * Rs\ 720,000[/tex]
Convert % to decimal
[tex]Total\ Income = Rs\ 12,500 + 0.005\ * Rs\ 720,000[/tex]
[tex]Total\ Income = Rs\ 12,500 + Rs\ 3,600[/tex]
[tex]Total\ Income = Rs\ 16,100[/tex]
Calculating his total sales if total income = Rs 20,000
Recall that;
[tex]Total\ Income = Salary + Commission[/tex]
Substitute Rs 20,000 for Total Income; Rs 12,500 for Salary and (0.5% of Monthly Sales) for Commission
[tex]Rs\ 20,000 = Rs\ 12,500 + 0.5\%\ of\ Monthly\ Sales[/tex]
Subtract Rs 12,500 from both sides
[tex]Rs\ 20,000 - Rs\ 12,500 = Rs\ 12,500 - Rs\ 12,500 + 0.5\%\ of\ Monthly\ Sales[/tex]
[tex]Rs\ 7,500 = 0.5\%\ of\ Monthly\ Sales[/tex]
[tex]Rs\ 7,500 = 0.5\%\ *\ Monthly\ Sales[/tex]
Divide both sides by 0.5%
[tex]\frac{Rs\ 7,500}{0.5\%} = \frac{0.5\%\ *\ Monthly\ Sales}{0.5\%}[/tex]
[tex]\frac{Rs\ 7,500}{0.5\%} = Monthly\ Sales[/tex]
Convert % to decimal
[tex]\frac{Rs\ 7,500}{0.5\%} = Monthly\ Sales[/tex]
[tex]\frac{Rs\ 7,500}{0.005} = Monthly\ Sales[/tex]
[tex]Rs\ 1,500,000 = Monthly\ Sales[/tex]
[tex]Monthly\ Sales = Rs\ 1,500,000[/tex]
how do you solve these problems?
Answer:
Step-by-step explanation:
Hello,
a. The area of region P is the area of the rectangle 1 * e minus the
[tex]\displaystyle \int\limits^0_1 {e^x} \, dx=[e^x]^{1}_{0}=e-1[/tex]
So this is e - (e-1) = e - e + 1 = 1
b. The area of region P is the area of the rectangle 1 * e minus P and minus the
[tex]\displaystyle \int\limits^0_1 {e^{-x}} \, dx=[-e^{-x}]^{1}_{0}=-e^{-1}+1[/tex]
So this is
[tex]e - 1 - (-e^{-1}+1) = e-1+e^{-1}-1=e+e^{-1}-2[/tex]
This is around 1.08616127...
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
PLEASE HELP THE QUESTION IS BELOW!!
Answer:
The answer is option D.
Their angles measures cannot be equal.
Answer:
D
Step-by-step explanation:
Hello,
What the question requires of us is just the property of complimentary angles and which is
The sum of their angles must be equal to 90°.
When two angles combine together to form angle 90°, it is said to be complimentary and they're referred to as a right angled triangle.
From the option, none of the angles can be up to a right angle triangle (90°)
The sum of their angles can be an acute triangle I.e 45°
45° + 45° = 90°
Knowing the fact that the angles can both be an acute angle (45°), it would be wrong to say both angles cannot be equal.
Hence option D is is wrong and it's the right answer in this case
PLEASE HELP The number of bagels sold daily for two bakeries is shown in the table: Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain. 1 Mean for both bakeries because the data is symmetric 2Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric 3 Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric 4 Median for both bakeries because the data is not symmetric
Answer:
4
Step-by-step explanation:
its unclear what the standard for "symmetric" is though both data points have large and small numbers ranging from the 10-40+ thus, the data range is large and the mean will not accurately represent the data well. Thus median would be best
Let P(A)=35 and P(B|A)=89. What is the probability of events A and B occurring?
I'm assuming you meant to say P(A) = 3/5 and P(B|A) = 8/9.
If so, then we multiply the probabilities to get P(A and B)
P(A and B) = P(A)*P(B|A)
P(A and B) = (3/5)*(8/9)
P(A and B) = (3*8)/(5*9)
P(A and B) = 8/(5*3)
P(A and B) = 8/15
Answer: 8/15Mr. Wilson invested money in two accounts his total investment was $8000. If one account pays 6% and interest and the other pays 12% interest how much did he invest in each account if he earned a total of $600 in an interest in one year
Answer:
Mr. Wilson invested $ 2,000 in the 12% simple interest account and $ 6,000 in the 6% simple interest account.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of the investment = $ 8,000
Interest rate of the first account= 6% simple
Interest rate of the second account= 12% simple
Interest of the accounts in a year = $ 600
2. How much did he invest in each account?
For answering the question, we will use the following equation:
x = Amount invested in the first account
8,000 - x = Amount invested in the second account
0.06x + 0.12 * (8,000 - x) = 600
0.06x + 960 - 0.12x = 600
-0.06x = 600 - 960 (Subtracting 960 at both sides)
-0.06x = -360
x = -360/-0.06
x = 6,000 ⇒ 8,000 - x = 2,000
Mr. Wilson invested $ 2,000 in the 12% simple interest account and $ 6,000 in the 6% simple interest account.